0=3x^3-432x

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Solution for 0=3x^3-432x equation:


Simplifying
0 = 3x3 + -432x

Reorder the terms:
0 = -432x + 3x3

Solving
0 = -432x + 3x3

Solving for variable 'x'.
Remove the zero:
432x + -3x3 = -432x + 3x3 + 432x + -3x3

Reorder the terms:
432x + -3x3 = -432x + 432x + 3x3 + -3x3

Combine like terms: -432x + 432x = 0
432x + -3x3 = 0 + 3x3 + -3x3
432x + -3x3 = 3x3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
432x + -3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(144 + -1x2) = 0

Factor a difference between two squares.
3x((12 + x)(12 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12

Subproblem 3

Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12

Solution

x = {0, -12, 12}

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